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Calculating exact roots of 6th degree polynomial

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Deepayan Bhadra
Deepayan Bhadra 2017 年 10 月 18 日
編集済み: Walter Roberson 2017 年 10 月 19 日
I've a fat 6x6 matrix E with symbolic variables. I'm trying to compute sqrt(eig(E'E)), ie, the singular values. The answer begins with 'root( ) etc. How do I get MATLAB to solve this 6th degree polynomial and show me more pleasing answers? Thanks a lot.

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Image Analyst
Image Analyst 2017 年 10 月 19 日
Use roots(), not root().
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Walter Roberson
Walter Roberson 2017 年 10 月 19 日
root() is the placeholder that replaced RootOf() a couple of releases ago in the Symbolic Toolbox.
Walter Roberson
Walter Roberson 2017 年 10 月 19 日
編集済み: Walter Roberson 2017 年 10 月 19 日
Which Galois group does it belong to? Because it is not generally possible to solve for exact algebraic roots.
https://en.wikipedia.org/wiki/Sextic_equation
By the way, have you ever looked at how long the roots are just for quartics? About 12500 characters per solution when using bare symbols for the coefficients; much much longer if the coefficients are expressions as you imply is happening for you.
Suppose you managed to find a (say) million character closed form for one of your eigenvalues: realistically, what would you do with it?

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